Mathematics II20785 marksRings and Fields
Define ring and show that set of real numbers with respect to addition and multiplication operation is a ring.
Define ring and show that set of real numbers with respect to addition and multiplication operation is a ring. [5]
An algebraic structure (R, +, ×) with two binary operations, addition (+) and multiplication (×), is called a ring if it satisfies the following conditions: R1. Closure under addition: a + b ∈ R, for all a, b ∈ R R2. Associativity of addition: a + (b + c) = (a + b) + c, for all a, b, c ∈ R R3. Ex...